1. Warm-up
1) write 3 positive and 3 negative solutions to the equation: 𝐜𝐨𝐬 𝒙 = 𝟑 𝟐 2) solve algebraically for 0≤𝑥≤360 𝟒 𝐬𝐢𝐧 𝒙 +𝟏𝟏=𝟏𝟒 3) solve with graphing calculator: give answers in radians 𝟓 𝐜𝐨𝐬 𝒙 =−.𝟖 4) find all solutions to the equation: 𝐬𝐢𝐧 𝜽 =−𝟏

2. Warm-up Identify the vertex of the parabola: 𝑦=2 (𝑥−5) 2 +6
Describe how each number of the equation above changes the graph, as compared to the graph of 𝑦= 𝑥 2

3. Trig Curves Transformed
Graphing a Cosine Functions
Draw one cycle of the function’s graph.
Amplitude
Period

4. Trig Functions Translation
Graphing a Reflection
Graph the function.
Amplitude
Period
Reflection over x-axis

5. Trig Functions Translation
Graphing a Reflection
Graph the function.
Amplitude
Period
Reflection over x-axis

6. Trig Functions Translation
Translations of Trigonometric Graphs
Translation of a Sine Function
Amplitude
Period

7. Rotating wheel problems
Spokeless ferris wheel in china: 276ft diam. 22min/rev

9. Vernal and Autumn Equinox
the time at which the sun crosses the plane of the equator towards the relevant hemisphere, making day and night of equal length. It occurs about March 21 in the N hemisphere (Sept 23 in the S hemisphere)
A year is days.

10. Wave phenomena

11. The electro-magnetic spectrum

15. Radio telescope

16. Radio telescope array

17. Trig Curves Transformed
Graph Sine, Cosine Functions

18. Trig Functions Translation
Translations of Trigonometric Graphs
Translation of a Sine Function
Amplitude
Period

19. Trig Functions Translation
Graphing a Vertical Translation
Graph the function.
Amplitude
Translation
down 2
Period

20. Trig Functions Translation
Graphing a Vertical Translation
Graph the function.
Amplitude
Translation
up 3
Period

21. Trig Functions Translation
Graphing a Horizontal Translation
Graph the function.
Amplitude
Period
Translation
right p

22. Trig Functions Translation
Graphing a Horizontal Translation
Graph the function.
Amplitude
Period
Translation
left p

23. Trig Functions Translation
Graphing a Horizontal Translation
Graph the function.
Amplitude
Period
Translation
right p/2

24. Transformations of sine and cosine
Period, Amplitude, phase shift, and vertical shifts

25. 𝟏𝟒𝟑° 𝟑𝟒° Inclination and Slope
The inclination of a line is the angle 𝑎 , where 0 𝑜 ≤𝑎< 180 𝑜 , that is measured from the positive x-axis to the line.
𝟏𝟒𝟑°
𝟑𝟒°

26. Theorem
For any line with slope 𝑚 and inclination 𝑎 𝑚= tan 𝑎 if 𝑎≠ 90 𝑜 .
If 𝑎= 90 𝑜 , then the line has no slope. (The line is vertical.)

27. 8.1 Simple Trigonometric Equations

29. Trig Curves Transformed
Homework
Sec odds